Natural optical activity as the origin of the large chiroptical properties in π-conjugated polymer thin films

Polymer thin films that emit and absorb circularly polarised light have been demonstrated with the promise of achieving important technological advances; from efficient, high-performance displays, to 3D imaging and all-organic spintronic devices. However, the origin of the large chiroptical effects in such films has, until now, remained elusive. We investigate the emergence of such phenomena in achiral polymers blended with a chiral small-molecule additive (1-aza[6]helicene) and intrinsically chiral-sidechain polymers using a combination of spectroscopic methods and structural probes. We show that – under conditions relevant for device fabrication – the large chiroptical effects are caused by magneto-electric coupling (natural optical activity), not structural chirality as previously assumed, and may occur because of local order in a cylinder blue phase-type organisation. This disruptive mechanistic insight into chiral polymer thin films will offer new approaches towards chiroptical materials development after almost three decades of research in this area.


Contents
Supplementary Methods Synthesis of c-PFO and c-PFBT

Supplementary Discussion 1 Mueller Matrix Spectroscopic Ellipsometry
The MM is written as a 4x4 matrix to describe transformation from incoming to outgoing Stokes parameters: The normalized MM for an isotropic sample or one without cross-polarization can be written in terms of N=cos(2), C=sin(2)cos(), and S=sin(2)sin() as, where  and  are the isotropic ellipsometry parameters.
For non-depolarizing materials, the differential Mueller Matrix can be written as follows: where CD: Circular dichroism, CB: Circular birefringence, LD: Horizontal LD, LB: Horizontal LB, LD': 45º LD, LB': 45º LB, A: Absorbance As can be seen above, CD and circular birefringence (CB) appear in the m14/m41 and m23/m32 elements of the differential Mueller matrix, respectively. The differential Mueller matrix (dMM) is calculated here as the matrix logarithm of the Mueller matrix [dMM=Log(MM)] which, in first approximation, can also be written as dMM≈I+MM, I being the 4x4 identity matrix. Therefore, Mueller matrix elements M14/M41 and M23/M32 are the key elements for the quantification of CD and CB, respectively.
Dielectric permittivity tensor for materials with uniaxial anisotropy:

Equation 4
Where  refers to the permittivity. In uniaxial media, two of the diagonal terms are the same, and one is different. In this case the z-axis is the extraordinary axis (whilst the x-and y-axes are ordinary).
Bragg reflection occurs when: where p is the pitchthe cholesteric-stack thickness required for molecules to make a complete turn (360°) To describe optical activity requires the complete 66 constitutive tensor that describes the complete electromagnetic interaction with the material and has the magneto-electric coupling terms in the off-diagonal blocks.
For materials obeying Lorentz reciprocity, the following relations are implied: The magneto-electric tensors can in general be written as = − and , = T − , where is the nonreciprocity or Tellegen tensor and is the chirality tensor. To satisfy the Lorentz reciprocity requirement above, it follows that = and ≠ must be fulfilled, where the latter relation is meant to imply that at least one of the tensor elements is not equal to zero. Transmitted Intensity and MM-Transmission data at normal incidence measured from a 130 nm thick F8T2:aza [6]H film were modeled using a cholesteric-stack like structure. The fit parameters included the extraordinary optical function while the ordinary optical function remained the same as from a neat polymer (a). The uniaxial optical axis was tilted into the sample surface plane and then allowed to rotate between the bottom and top of the film. The total rotation in degrees was fit to match the circular features in the data. For this purpose, only the M22, M33, M14, M41, M23, and M32 elements were used for fitting (b). The final fit result is shown below: 162° of twist and strong uniaxial anisotropy was able to match the Transmitted data sets. The model uses the ordinary optical functions for F8T2 from the neat polymer and allows the extraordinary values to be fit along with the total twist in the helical structure (modeled here as 0.45 twists). This model is then used to calculate and compare to the reflected MM values from the same sample. As can be seen, the chiral model produces strong CD and CB behavior while our measured data only exhibits a very weak response in reflection.  and (2) a coherent (domains < the wavelength of light) superposition. We should note, at present there are no experimental control samples to validate the outputs of either model. We find that the coherent superposition (2) of randomly oriented, sub-micron, partially formed cholesteric domains (i.e. not fully complete twists) can result in MMSE spectra without circular elements, but only at certain angles of incidence. The model does not hold when multiple angles of incidence are considered, and we see no evidence of such grains through spatially resolved MMSE/CD. Therefore, we do not believe that a multi-domain cholesteric structure is present in the unaligned polyfluorene systems considered here.

Incoherent superposition of 'large' domains
To establish whether a multi-domain or 'mosaic' cholesteric liquid crystal structure could be responsible for the strong chiroptical phenomena recorded here, a model was created that allowed mixing of multiple domains with ability to vary their 1) starting orientation, 2) amount of twisting, and 3) tilt angle. Of these three effects, calculations with multiple "starting orientations" can effectively minimize the linear response for transmitted measurements, while maintaining the circular response.  Measured transmission depolarisation index (pink line) and the predicted depolarisation index for single (black line) and multi-domain (blue line) systems.

Details of the multi-domain model that modifies for starting orientation.
Whilst a multi-domain model that only makes use of multiple starting orientations can minimise the linear terms of transmission measurements, it does not suppress the circular response of the reflection spectra.
Instead, we found a combination of all three (i.e. a calculation that allows for starting orientation, amount of twist, and tilt angle) can suppress the circular response. However, it would suppress the circular response for both transmitted and reflected beams and would lead to significant depolarization.

Details of the multi-domain model that modifies for starting orientation, amount of twist and tilt angle.
Reflection M14 (CD) and M23 (CB) terms predicted using the multi-domain model.

Measured reflection depolarisation index (pink and blue lines) and the modelled depolarisation index for a single (a) and multi-domain (b) cholesteric stack.
Transmission MMSE spectra recorded for annealed F8BT:aza[M] films and the predicted spectra from a model that controls for the 1) starting orientation, 2) amount of twist, and 3) tilt angle. In summary, we have not been able to find a model based on a multi-domain system that simultaneously satisfies all the experimental observations: 1) suppress the linear anisotropic responses that would be obtained in transmission MMSE measurements, 2) suppress the circular anisotropic responses that would be obtained in reflection MMSE measurement, 3) maintain the chiroptical response in transmission (not only at normal incidence but also at oblique incidence) and 4) not introducing significant depolarization.

Coherent superposition of 'small' domains
Having failed to successfully simulate the optical response using a where cn is a weighting factor associated with each individual grain (n th Jones matrix) and rpp, rsp, rps, and rss represent the complex Fresnel coefficients for the n th model. Above we describe the general approach that underpin this multi-domain analysis; the coherent mixing of 4 grainswhere each model represents a grain with a twisted anisotropic structure and a different starting orientation. For each grain, the total amount of twist can vary along with film thickness and anisotropic optical constants to fit the MM data in reflection (25°) and transmission (0°). Anisotropic optical constants were allowed to vary in both directions but constrained by Kramers-Kronig consistent oscillator summations.
Below we show the MMSE data collected in transmission (MMt, angle of incidence 0°) and reflection (MMr with different starting orientations. If the data averaged more grains of one orientation than another, then cancellation would not be complete, and we would see a preferential circular response in reflection. (a)
Based on this data, we can draw the following conclusion. For the cancellation to be effective, the twisted structures need to "balance" each other out with complementary starting orientations. For example, a starting orientation of 0° can be balanced with a starting orientation of 90°. It is very unlikely that there are a small number of starting orientationsespecially since the in-plane anisotropy of this twisted model also produces linear optical responses which need to be smeared out (in addition to the circular responses). It is more likely that the coherent models would be a collection of random orientations and possibly random tilt angles relative to the surface.
Informed by the coherent multi-domain model described above, we compared the simulated and experimental transmission data at variable angles (transmission, MMt; 0°, 30° and 60° and reflection, MMr; 25° and 60°).
If multiple angles of incidence are considered; the coherent multi-domain model fails to fit all data together. This implies that this multidomain model is not compatible with the overall uniaxial response seen on the sample.

Experimental and simulated transmission (a) and reflection (b) MMSE spectra acquired at multiple angles of incidence (a)
In order to further experimentally investigate whether the optical response from such a multi-domain structure exists within our samples, we mapped the uniformity of the circular terms in reflectance (65°) using a 40 µm beam over 1200 points on a 0.8 mm × 0.8 mm area. Whilst this is by no means a sub-micron measurement, if the grain sizes are in the micron-range then such a focused measurement should show varying circular effects when not perfectly "cancelled". The grey circles (the vertical line along x = 0) were selected to compare spectra.
As can be seen below, there is no indication of large grains such as those described above (the circular response of single grains) where the circular response would not maintain "balance" at different locations. In other words, any proposed multi-grain model would need to contain a large number of smaller grains to smear-out the circular reflected response in a similar manner at each of these points. Comparable to the spatially resolved CD spectra acquired at the Diamond Light Source (Supplementary Figure   2), the response is incredibly uniform. In fact, the new, high resolution, spatially resolved spectroscopic data above perfectly fits the 6 × 6 model described in Equation 2 which incorporates magneto-electric coupling (i.e., natural optical activity).
Simulated circular terms (a, MM14, B, MM23) spectra in reflection (65°) using the 6 × 6 magneto-electric coupling model We have also measured transmission and reflection MMSE data for ultra-thick films (915 nm), which should be closer to a 'Bragg reflector' (Figure 10). Even at these thicknesses, there is no circular selective response in reflection.

Transmission (a) and reflection (b) MMSE spectra recorded for a 915 nm thick F8BT:aza[6]H (P) film
Supplementary Figure 9 Anisotropic gyrotropic terms for annealed ACPCA thin films We note that a model based on an isotropic optical activity tensor (i.e. x z   ) cannot explain well the results obtained at oblique angles. This fact becomes especially evident when trying to fit simultaneously transmission measurements at both normal incidence (0°) and at the most oblique measurement angle (60°) as shown below: Model fits to the transmitted MMSE data recorded at three different sample orientations from aligned cPFBT films using an optical model that makes use of structural chirality.

Transmitted MMSE
Model fits to the transmitted MMSE data recorded at three different sample orientations (0, 45 and 90°) from aligned cPFBT films using an optical model that makes use of structural chirality.
Fits to the reflected MMSE data recorded at 70° angle from three different orientations (0, 45 and 90°) of the aligned cPFBT films using an optical model that makes use of structural chirality.
The fit utilizing structural chirality is also able to reproduce the reflected MMSE data recorded at 30° angle of incidence from aligned cPFBT films as a function of sample rotation.
The fit utilizing structural chirality is also able to reproduce the reflected MMSE data recorded at 70° angle of incidence from aligned cPFBT films as a function of sample rotation.
Transmitted MMSE: The fit utilizing structural chirality is mostly able to reproduce the transmitted MMSE data recorded at normal incidence (0°) from aligned cPFBT films as a function of sample rotation.

Full model
The final fit utilizing biaxial anisotropy and structural chirality was matched to MMSE data in both transmission and reflection versus angle of incidence and at three different sample orientations.

Reflection MMSE:
A twisting model was not adequate and strongly suggests the combination of both twisting phenomena and natural optical activity.

Supplementary Figure 14 RSoXS for as-cast and annealed ACPCA thin films
RSoXS measurements are performed in a transmission geometry using a soft x-ray scattering beam line. The X-ray photon energy (E = 283.5 eV) was resonant with the carbon K-edge. The neat and as-cast ACPCA thin films ((a) -(d)) demonstrate features characteristic of uniaxial anisotropy but no detectable Bragg scattering. On the other hand, the scattering patterns in the annealed ACPCA thin films ((e), (f)) indicate that the polymer chain is arranged in a periodic structure, where characteristic length scales (x) can simply be extracted from the peak wave vector (qH) for Bragg scattering.

Supplementary Discussion 3 of AFM measurements
To probe the organisation at the air-film interface of the annealed thin films, tapping mode (AC mode) atomic force microscopy (AFM) was carried out under ambient conditions. The surface of the annealed and unaligned F8BT-based ACPCA film (Figure 5a) is very smooth, with a roughness (RMS) value of 0.49 nm (calculated over a 1.0 µm 2 scan area). In the absence of the chiral aza [6]H additive (Fig. 5b) the surface has a higher roughness, 0.81 nm RMS. The lower roughness of the ACPCA film is also evident in the height profiles (Figs. 5c and 5d).
A comparison between the topography images of the annealed pure F8BT polymer and the blend with the azahelicene (Figure 5a and 5b) reveals that a fibril-like organisation is particularly evident for the sample with the chiral additive, and, though present in the pure F8BT is less well resolved without the chiral additive.
Overall  In situ circular dichroism spectra for cPFBT during heating and cooling and the maximum CD of the lowest energy transition during the first (a) and second (b) heating/cooling cycle.
In situ circular dichroism spectra for cPFO during heating and the maximum CD of the lowest energy transition during the first (top row) and second (bottom row) heating/cooling cycle.

Supplementary Discussion 5: in situ CD measurements
Using the temperature at which we obtain the strongest CD (TCD Max, extracted from the in situ temperature dependent CD measurements described above, Figure 7, Supplementary Figures 17 -21), we investigated the annealing time required to induce the strongest chiroptical response in 120 nm thick films ( Figure 7, Supplementary Figures 19 -S21, Supplementary Figure 23). The chiroptical effect is induced very quickly; within 300 seconds of being held at TCD Max for PFO, 20 seconds for F8T2, 800 seconds for F8BT and 180 seconds for both the CSCP thin films.
Of the ACPCA thin films considered in this study, the strongest chiroptical effect at room temperature is observed in the F8T2 : aza [6]H films, where CD ≈ 19,500 mdeg and represents the highest reported chiroptical effect in polymer thin films, and the weakest in PFO : aza [6]H films, where CD ≈ 3,100 mdeg ( Figure 2). This may be due to the relative flexibility of the thiophene units, reduced density of sidechains resulting in more homogeneous conformation of polymer backbones, or differences in the chemical composition of the polymers. [24][25][26] In the case of the ACPCA thin films, in situ CD ( Figure 5) indicates that below 200 C there are two phases with strong chiroptical properties within F8BT and PFO, one kinetic chiral structure that forms at TCD Max with high CD, but does not persist upon elevating the temperature or repeat heating/cooling cycles. The other structure seems more thermodynamically robust, with lower CD, that forms when T > TCD Max and persists. In contrast, for F8T2 only one high intensity CD chiral phase forms, which is thermodynamically stable up to 200 C, and is stable to further heating cycles. Regardless, the mirror symmetry of the temperature-and time-dependent CD spectra for the ACPCA thin films with [P] and the [M] enantiomers of the chiral additive (Figure 7), and absence of any aza [6]H signature in the chiroptical response, indicates that the aza [6]H acts as a chiral seed to template the handedness of the polymer chiral structure. For the CSCPs, there exists only one high intensity CD stable chiral phase below 200 C that forms when T = 140 C (Supplementary Figure 16). These results indicate that both approacheschiral additive versus chiral sidechainallow for a complementary means to achieve chiral polymer films with very large CD due to natural optical activity. To quantitively assess the optical activity of aligned and non-aligned ACPCA and CSCP thin films annealed at TCD Max we calculated the dissymmetry factor, gabs, by normalising the CD (∆A) to the unpolarised absorbance of the sample. To better understand the origins of this chiroptical response, we controlled the spincoating speed to fabricate a series of thin films with different thicknesses. In such films, the competition of different aggregation pathways may result in the formation of various polymorphs in principle. However, the variable thickness ACPCA films considered here suggest that this is not the case for these materials, with similar shaped CD profiles for thick and thin films and no evidence of different polymorphs in AFM or crosspolarised optical microscopy images. 21 At first glance, the g-factors of all systems (aligned and not-aligned, ACPCA and CSCP) appear to increase as a function of film thickness (i.e. thicker films achieve higher gabs than thin films). To accommodate for reflection losses at the interfaces, we followed the simple protocol introduced by Schiek et al. 7 Once reflection losses are accounted for, the non-aligned thin films have a thickness independent gabs, whereas aligned thin films show a gabs that increases linearly as a function of film thickness. Clearly, this thickness-dependent dissymmetry of aligned systems (i.e. where structural chirality dominates) should tend to zero for very thin films, but in the cases considered here, we believe both natural optical activity and structural chirality contribute to the measured chiroptical response.

Supplementary
We should note that the large g-factors observed for these systems contrast the small effects typically seen for small molecules. In the case of small molecules, the g-factor can be calculated from 27 ; Where µ is the electric transition dipole moment, m the magnetic transition dipole moment, R the rotational strength and D the dipole strength of an electronic transition from i-j. Based on Supplementary Equation 10 and the large µs of fluorene polymers, g-factors > 1 would require unrealistically large magnetic transition dipole moments. However, the well-known expression for g-factor (i) assumes isolated, non-interacting chromophores, (ii) assumes molecules that are much smaller than the wavelength of light and (iii) neglects